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In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…
In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions…
In this manuscript, we address continuous unconstrained multi-objective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we analyze the class of Front Descent methods, which…
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes…
In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus…
In this paper, we propose a simple yet efficient strategy for improving the multi-objective steepest descent method proposed by Fliege and Svaiter (Math Methods Oper Res, 2000, 3: 479--494). The core idea behind this strategy involves…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used.…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
Stochastic multi-objective optimization (SMOO) has recently emerged as a powerful framework for addressing machine learning problems with multiple objectives. The bias introduced by the nonlinearity of the subproblem solution mapping…